OFFSET
1,7
COMMENTS
The Bell transform of A033678(n+1). For the definition of the Bell transform, see A264428. - Peter Luschny, Jan 17 2016
LINKS
Alois P. Heinz, Rows n = 1..45, flattened
FORMULA
EXAMPLE
T(3,1) = 1 counts the complete graph on 3 labeled vertices.
T(3,3) = 1 counts the empty graph (no edges) on 3 labeled vertices.
Triangular array T(n,k) (with rows n >= 1 and columns k = 1..n) begins:
1;
0, 1;
1, 0, 1;
3, 4, 0, 1;
38, 15, 10, 0, 1;
720, 238, 45, 20, 0, 1;
...
MATHEMATICA
nn = 8; e = Sum[2^Binomial[n - 1, 2] x^n/n!, {n, 1, nn}];
Prepend[Drop[Map[Insert[#, 0, -2] &,
Map[Select[#, # > 0 &] &,
Range[0, nn]! CoefficientList[
Series[(e + 1)^y, {x, 0, nn}], {x, y}]]], 2], {1}] // Grid
PROG
(Sage) # uses[bell_matrix from A264428]
# Adds a column 1, 0, 0, 0, ... at the left side of the triangle.
bell_matrix(lambda n: A033678(n+1), 9) # Peter Luschny, Jan 17 2016
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Geoffrey Critzer, Aug 27 2013
STATUS
approved